Answer:
I believe the correct answer from the choices listed in the image is the second option. The statement that allows us to conclude that line m and line n are parallel would be that angle 2 and angle 7 are equal. They are alternate exterior angles. Hope this answers the question.
Answer:
D. (4x - 1)(4x + 1)
Step-by-step explanation:
16 is a perfect square, with its two identical factors being 4. 1 is also a perfect square, with its two factors being 1, but in this case, it's a -1, so we need a positive 1 and a negative 1:
(4x + 1) (4x - 1)
Answer:
![58, 68, 68, 68, 74, 74, 76, 77, 78, 79](https://tex.z-dn.net/?f=58%2C%2068%2C%2068%2C%2068%2C%2074%2C%2074%2C%2076%2C%2077%2C%2078%2C%2079)
Step-by-step explanation:
Given
![n=10](https://tex.z-dn.net/?f=n%3D10)
![Mean = 72](https://tex.z-dn.net/?f=Mean%20%3D%2072)
![Median = 74](https://tex.z-dn.net/?f=Median%20%3D%2074)
![Mode = 68](https://tex.z-dn.net/?f=Mode%20%3D%2068)
![Range = 21](https://tex.z-dn.net/?f=Range%20%3D%2021)
Required
The complete dataset
The question has missing options (available online)
From the mean, we have:
![Mean = \frac{\sum x}{n}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
This gives:
![72 = \frac{\sum x}{10}](https://tex.z-dn.net/?f=72%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7B10%7D)
Cross multiply
![\sum x = 72 * 10](https://tex.z-dn.net/?f=%5Csum%20x%20%3D%2072%20%2A%2010)
![\sum x = 720](https://tex.z-dn.net/?f=%5Csum%20x%20%3D%20720)
<em>This means that the sum of all elements of the dataset is 720</em>
Next, we test the median
Since n = 10, then:
![Median = \frac{n + 1}{2}](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7Bn%20%2B%201%7D%7B2%7D)
![Median = \frac{10 + 1}{2}](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7B10%20%2B%201%7D%7B2%7D)
![Median = \frac{11}{2}](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7B11%7D%7B2%7D)
![Median = 5.5th](https://tex.z-dn.net/?f=Median%20%3D%205.5th)
This implies that the median is the average of the 5th and 6th item.
So, we have:
![Median = \frac{5th + 6th}{2}](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7B5th%20%2B%206th%7D%7B2%7D)
Cross multiply
![5th + 6th = 2 * Median](https://tex.z-dn.net/?f=5th%20%2B%206th%20%3D%202%20%2A%20Median)
![5th + 6th = 2 * 74](https://tex.z-dn.net/?f=5th%20%2B%206th%20%3D%202%20%2A%2074)
![5th + 6th = 148](https://tex.z-dn.net/?f=5th%20%2B%206th%20%3D%20148)
<em>This means that the 5th and 6th element add up to 148</em>
Also, we have:
![Mode = 68](https://tex.z-dn.net/?f=Mode%20%3D%2068)
<em>This means that 68 has to appear at least twice in the dataset</em>
<em>This implies that the difference between the highest and the least is 21.</em>
The dataset that satisfies the above condition is:
![58, 68, 68, 68, 74, 74, 76, 77, 78, 79](https://tex.z-dn.net/?f=58%2C%2068%2C%2068%2C%2068%2C%2074%2C%2074%2C%2076%2C%2077%2C%2078%2C%2079)
Answer:
280 ft
Step-by-step explanation:
An auditorium is in the shape of an equilateral triangle with side length as 112 ft.
The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.
*The situation is represented in the attachment.
According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
Hence, the length of the mid-segment in this case is,
![\dfrac{1}{2}\times 112=56\ ft](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20112%3D56%5C%20ft)
Therefore, the perimeter of the seating area is,
![=112+56+56+56=280\ ft](https://tex.z-dn.net/?f=%3D112%2B56%2B56%2B56%3D280%5C%20ft)